Engineering topics

Lin, D. N. C.

Publications and source records attributed to Lin, D. N. C..

54 records · Page 3

NASA NTRS1988

Collisional properties of ice spheres at low impact velocities

The results of experimental studies on the impact properties of water ice are discussed. Stable temperatures of 85 K and pressures as low as 10 to the -5th Torr were achieved using a new apparatus consisting of a compound disk pendulum and a stainless steel, temperature-controlled cryostat. The coefficient of restitution as a function of velocity was obtained for ice spheres with four different radii of curvature and with a variety of surface conditions. These data can be well fitted by an exponetial law epsilon of given form for most measurements. Surface conditions can drastically alter the resulting value of epsilon, however. In particular, the presence of frost or a roughened contact surface can lower epsilon at a given velocity by 10-30 percent from that of a smooth sphere. It is shown how the presence of frost can change the velocity behavior of epsilon from an exponential to a power-law form. The applications of the results to the dynamics of Saturn's rings are discussed.

Hatzes, Artie P.↗

NASA NTRS1988

On the collapse and violent relaxation of protoglobular clusters

During the formation of stellar systems such as globular clusters, low-mass subcondensations which eventually form stars must retain a geometric size throughout the collapse process that is small compared to the characteristic distance separating them. If the local velocity dispersion of the subcondensations is small, the overall dimension of the system can decrease substantially before reaching a dynamical equilibrium state. The maximum collapse factor is deduced by examining the growth of the velocity dispersion and the spread in arrival times at the origin caused by local and global fluctuations. It is shown, analytically as well as in a series of N-body simulations, that the maximum reduction in the characteristic dimension of a system of N fragments with an initial homogeneous distribution subject to N exp 1/2 fluctuations is proportional to N exp 1/3. Direct physical collisions between low-mass subcondensations are therefore unlikely to occur in protoglobular clusters. The results are discussed in the context of fragmentation and violent relaxation.

Aarseth, S. J.↗

NASA NTRS1988

Thermal limit cycles in supermassive accretion disks

Interpretations of the quasi-periodic outbursts of dwarf novae in terms of a thermal-viscous limit cycle mechanism operating in the accretion disk are discussed. Numerical solutions to vertical equilibrium equations are used to show that the limit cycle mechanism should occur in supermassive disks. The mechanism acts as a gate that modulates the rate of accretion reaching small radii, where most of the luminosity is produced. Formulas are derived for the period and outburst luminosity in terms of the black hole mass and the radius at which the unstable zone occurs.

Shields, G. A.↗

NASA NTRS1987

The formation of the exponential disk in spiral galaxies

A mechanism for the formation of the exponential stellar disk distribution in spiral galaxies is proposed. It is assumed that the gas which falls in to form the disk behaves like an accretion disk which evolves on a viscous time scale t(v) and forms stars on a time scale t(star). It is demonstrated that if t(v) roughly equals t(star) the resulting stellar disk has an exponential distribution independent of the disk rotation law and of the assumed viscosity prescription. Why the viscous and star formation time scales might be related is briefly commented on.

Lin, D. N. C.↗

NASA NTRS1987

On the confinement of planetary arcs

The necessary conditions for planetary arc confinement are investigated, concentrating on the limiting case where the arc is marginally confined. It is shown that periodic perturbations due to a discrete Lindblad resonance can induce a secular change of Jacobian energy as well as orbital eccentricity. If the particles are subject to the perturbation of only one inner (outer) Lindblad resonance, the Lindblad resonance's location must be exterior (interior) to that of the corotation resonance if the perturbations are to lead to confinement. The trajectories of particles that are subject to inelastic collisions and pertubations due to corotation and Lindblad resonances are computed, showing that the confinement mechanism can indeed operate provided the perturbation due to the Lindblad resonance is sufficiently strong to balance viscous effects. The possibility that internal nonradial oscillations of Neptune may provide the necessary perturbations for arc confinement is considered.

Lin, D. N. C.↗

NASA NTRS1987

Experimental studies on the impact properties of water ice

Experimental studies on the impact of ice particles at very low velocity were continued. These measurements have applications in the dynamics of Saturn's rings. Initially data were obtained on the coefficient of restitution for ice spheres of one radius of curvature. The type of measurements were expanded to include restitution data for balls with a variety of surfaces as well as sticking forces between ice particles. Significant improvements were made to this experiment, the most important being the construction of a new apparatus. The new apparatus consists of a smaller version of the disk pendulum and a stainless steel, double-walled cryostat. The apparatus has proved to be a significant improvement over the old one. Measurements can now be made at temperatures near 90 K, comparable to the temperature of the environment of Saturn's rings, and with much greater temperature stability. It was found that a roughened contact surface or the presence of frost can cause a much larger change in the restitution measure than the geometrical effect of the radius of curvature.

Bridges, F. G.↗

NASA NTRS1987

A viscosity prescription for a self-gravitating accretion disc

A model for treating the transfer of angular momentum within a gaseous differentially rotating disc subject to gravitational instability is discussed in terms of an effective kinematic viscosity. It is assumed that even when matter in the disc is subject to self-gravitation, the instability does not necessarily lead directly to condensation of parts of the disc into self-gravitating bodies. Conditions under which the present model permits a similarity solution are discussed, and it is shown that the general solution tends to the similarity solution at large times.

Lin, D. N. C.↗

NASA NTRS1986

On the tidal interaction between protoplanets and the protoplanetary disk. III - Orbital migration of protoplanets

The tidal interaction between a protoplanet and a gaseous protoplanetary disk is investigated, and the dynamical evolution of the disk and the orbital migration of the protoplanet in a self-consistent manner is considered. It is shown that the orbital migration of a protoplanet does not suppress the tendency for tidal truncation in the vicinity of its orbit. If the necessary condition for tidal truncation is satisfied, the protoplanet induces a tidal feedback mechanism that regulates the rate of angular momentum transfer between the protoplanet and the disk. Significant orbital migration can only occur on the viscous evolution time scale of the disk.

Lin, D. N. C.↗

NASA NTRS1986

The global evolution of the primordial solar nebula

Complete radial, time-dependent calculations of the structure and evolution of the primordial solar nebula during the viscous diffusion stage are presented. The viscous stress is derived from analytic one-zone models of the vertical nebular structure based on detailed grain opacities. Comparisons with full numerical integrations indicate that the effective viscous alpha parameter is about 0.01. The evolution time of a minimum mass nebula is one-million yr or less. The flow pattern of fluid elements in the disk is examined and the implications the results have on the theory of the formation of the solar system are discussed.

Ruden, S. P.↗

NASA NTRS1986

On the tidal interaction between protoplanets and the primordial solar nebula. II - Self-consistent nonlinear interaction

A method to analyze the full nonlinear response and physical processes associated with the tidal interaction between a binary system and a thin disk in the steady state is presented. Using this approach, density wave propagation, induced by tidal interaction, may be studied for a wide range of sound speeds and viscosities. The effect of self-gravity may also be incorporated. The results of several calculations relevant to the tidal interaction between a protoplanet and the primordial solar nebula are also presented.

Lin, D. N. C.↗

NASA NTRS1986

On star formation in stellar systems. I - Photoionization effects in protoglobular clusters

The progressive ionization and subsequent dynamical evolution of nonhomogeneously distributed low-metal-abundance diffuse gas after star formation in globular clusters are investigated analytically, taking the gravitational acceleration due to the stars into account. The basic equations are derived; the underlying assumptions, input parameters, and solution methods are explained; and numerical results for three standard cases (ionization during star formation, ionization during expansion, and evolution resulting in a stable H II region at its equilibrium Stromgren radius) are presented in graphs and characterized in detail. The time scale of residual-gas loss in typical clusters is found to be about the same as the lifetime of a massive star on the main sequence.

Tenorio-Tagle, G.↗

NASA NTRS1986

Compton-heated winds and coronae above accretion disks. II - Instability and oscillations

The stability and evolution of windy accretion disks is investigated in detail. The basic disk evolution equations are briefly recapitulated, and an idealized analytic treatment of the wind and viscosity is used to show that steady disk flow is indeed unstable for sufficiently large ratio of the mass loss rate in the wind to the central accretion rate. Numerical solutions for a more realistic and appropriate expression for the mass loss rate and the standard ad hoc alpha model prescription for the viscosity are presented. The application of these results to real systems with Compton-heated winds is discussed, and a general formula for the oscillation period is given. The prediction is compared with observed periodic behavior of Galactic X-ray sources and AGNs.

Shields, G. A.↗

NASA NTRS1986

Accretion disks and periodic outbursts of active galactic nuclei

The local thermal stability of accretion disks around supermassive black holes in active galactic nuclei is examined. Such disks are unstable at radii where the surface temperature is several thousand degrees. Supermassive disks therefore should undergo limit-cycle outbursts similar to those believed to occur in dwarf novae. Operating on a time scale of about 10,000 to 10 million yr and at radii of about 10 to the 15th to 10 to the 16th cm, this mechanism will result in alternating periods of higher and lower accretion rate onto the black hole and, consequently, higher and lower luminosity. Quasi-periodic outbursts on this time scale may be recorded in the structure of extended radio sources, a possible example being 4C 29.47. For accretion rates greater than 0.1 solar masses/yr, the situation is complicated by instabilities caused by self-gravitation and by the dominance of radiation pressure and electron scattering opacity.

Lin, D. N. C.↗

NASA NTRS1985

On the evolution of accretion disc flow in cataclysmic variables. III - Outburst properties of constant and uniform-alpha model discs

Attention is given to the stability and evolution of some simple accretion disk models in which the viscosity is prescribed by an ad hoc, uniform-alpha model. Emphasis is placed on systems in which the mass input rate from the secondary to the disk around the primary is assumed to be constant, although initial calculations with variable mass input rates are also performed. Time-dependent visual magnitude light curves constructed for cataclysmic binaries with a range of disk size, primary mass and mass input rate, and viscosity magnitude, are compared with the observed properties of various cataclysmic variable subclasses. The results obtained indicate that the observational differences between novae and dwarf novae may be due to mass input rate differences. The present models can reproduce the gross observational features of U-Gem-type dwarf nova outbursts.

Lin, D. N. C.↗

NASA NTRS1984

The evolution of the inner regions of viscous accretion disks surrounding neutron stars

The structure and evolution of the inner regions of an accretion disk around a neutron star have been investigated with respect to variations in the mass flow rate. In order to examine the sensitivity of the general response of the disk to the form of viscous dissipation, several theoretical constraints on disk evolution are proposed on the basis of current accretion disk theory. It is shown through a series of calculations that under certain circumstances nonlocal radial energy transfer can stabilize regions of the disk which appear to be unstable by local analysis. When viscous stress was scaled with the total pressure of the disk, global analysis was found to be consistent with local analysis, and instability was manifested in luminosity fluctuations and in bursts of less than 10 s. Analysis of the bursts in their limit cycles showed that the disk remained optically thick and geometrically thin throughout its evolution. Substantial agreement was found between the theoretical results and the available observational data.

Taam, R. E.↗

NASA NTRS1984

Collision-induced transport processes in planetary rings

The physics of collision-dominated particle disks around planets is analyzed from both the analytical and numerical point of view. The existence of Saturn's ringlet structure is analyzed in terms of a radial instability induced by viscous diffusion. The detailed model described is based on the assumption of uniform particle size. Modifications caused by finite particle size, gravitational effects, and a distribution of particle sizes are discussed.

Stewart, G. R.↗

NASA NTRS1983

Numerical simulations of the decay of satellite galaxy orbits

A multiple three-body technique is used to study the orbital evolution of satellite galaxies which is similar to the N-body method but neglects two-body forces between stars in the halo of the parent galaxy. It is found that, for satellites orbiting within the halo, Chandrasekhar's (1960) dynamical friction formula accurately describes the orbital decay rate, including its variation with satellite mass and size and with the number density and mass of halo stars. Significant frictional forces are present even outside the halo, and the orbital decay rate, instead of depending on the procedure used to place the satellite in its orbit, is determined only by the current orbital parameters. This semirestricted N-body method is sufficiently fast to have permitted the running of 200 simulations to date, many more than would have been possible by means of the conventional N-body technique.

Lin, D. N. C.↗

NASA NTRS1980

Tidal torques on infrequently colliding particle disks in binary systems and the truncation of the asteroid belt

Conditions leading to the truncation, at the 2:1 resonance, of a disk of infrequently colliding particles surrounding the primary of a binary system are studied numerically and analytically. Attention is given to the case in which the mass ratio, q, is sufficiently small (less than about 0.1) and the radius of the disk centered on the primary allowably larger, so that first-order orbit-orbit resonances between ring material and the secondary can lie within it. Collisions are found to be less frequent than q to the -2/3 power orbital periods (the period of the forced eccentricity at the 2:1 resonance), and truncation occurs and Kirkwood gaps are produced only if the particle eccentricity is less than some critical value, estimated to be of order q to the 5/9 power, or approximately 0.02 for the sun-Jupiter case having q equal to 10 to the -3rd power.

Franklin, F. A.↗